Transcript intro.phys.psu.edu

Golden Ratio
Jingting Zhao
Tianxin Li
Congya Tan
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What is Golden Ratio
The Golden Ratio illustrates a relationship that
a+b is to a as a is to b, a>b>0. In this
relationship, a: b = (a+b): a = 1.61803 39887
49894 84820. It is considered truly unique in
its mathematical properties, its prevalence
throughout nature, and its ability to achieve a
perfect aesthetic composition. (April Holloway)
image source:en.Wikipedia: Golden ratio line.png
The Discovery
It is unknown exactly when it was first discovered. It is
reasonable to assume that it has perhaps been discovered
and rediscovered throughout history, which explains why it
goes under several names (Gary Meisner, 2012). (e.g.,
Golden Ratio, Golden Section, Divine Proportion, phi)
The Discovery
We know the first recorded definition of the golden ratio
dates back to the period when Greek mathematician, Euclid
(c. 325–c. 265 BC), described what he called the "extreme
and mean ratio".(2013, April Holloway)
In “Elements” it stated: "A straight line is said to have been
cut in extreme and mean ratio when, as the whole line is to
the greater segment, so is the greater to the lesser."(2007,
Fitzpatrick (translator))
Prevailing View
Before the golden ratio was discovered, artists and
architects had little guidance about how to create
aesthetically pleasing art. They draw paintings and
construct buildings based on their own understanding
of beauty, which may not be as aesthetic as others
see them. And because of that, there was much less
work produced during this period than renaissance
period where golden ratio had been discovered and
widely used by artists and architects.
Prevailing View
As for individuals, people used to judge beauty
merely on one’s own perspectives and did not have a
tool or a standard measurement to conclude which
work was better.
Social Impact
The discovery of golden ratio revealed people’s sense of
beauty in scientific manner, which also provided a viable
standard measurement for people to assist them when
appreciating and creating art work.This especially had
great impact on the design of architecture. We can find
the application of golden ration in lots of world famous
architectures.
Social Impact
Notre Dame in Paris,
which was built in
between 1163 and
1250, appears to
have golden ratio
proportions in a
number of its key
proportions of
design.
green
blue
red
Social Impact
Notre Dame
Red – Vertical height of base at ground
level : Top of first level : Top of second floor
Blue – Vertical height of base of second
level : Top of second level : Top of third
level
Green – Horizontal width of outside of left
top section : Top right section : Top right
section
Social impact
Renaissance artists of the
1500’s in the time of Leonardo
Da Vinci knew it as the Divine
Proportion. In India, it was used
in the construction of the Taj
Mahal, which was completed in
1648.
Social impact
The United Nations building
also reflects the golden ratio
in a number of aspects of its
design.
Social impact
The CN Tower in Toronto has
contains the golden ratio in its
design. The ratio of observation deck
at 342 meters to the total height of
553.33 is 0.618, which is the
reciprocal of golden ratio.
Bibliography
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"῎Ακρον καὶ μέσον λόγον εὐθεῖα τετμῆσθαι λέγεται, ὅταν
ᾖ ὡς ἡ ὅλη πρὸς τὸ μεῖζον τμῆμα, οὕτως τὸ μεῖζον πρὸς
τὸ ἔλαττὸν" as translated in Richard Fitzpatrick
(translator) (2007). Euclid's Elements of Geometry.
ISBN 978-0615179841. , p. 156
April Holloway (December 5, 2013). The Golden Ratio
– a sacred number that links the past to the present.
Retrieved from http://www.ancientorigins.net/unexplained-phenomena/golden-ratiosacred-number-links-past-present-001091
Bibliography
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H. E. Huntley (June 1, 1970) The Divine Proportion: A
Study in Mathematical Beauty (Dover Books on
Mathematics). Dover Publications; 1st edition.
M. Gary(2012) History of the Golden Ratio.
Retrieved from http://www.goldennumber.net/goldenratio-history/
M. Gary (2013). Phi and the Golden Section in
Architecture. Retrieved from
http://www.goldennumber.net/architecture/
Bibliography
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McVeigh, Karen. "Why Golden Ratio Pleases
the Eye: US Academic Says He Knows Art
Secret." Theguardian. Theguardian.com, 28
Dec. 2009. Web. 28 Feb. 2015.
Meisner, Gary. "Golden Ratio Properties,
Appearances and Applications Overview."
Phi 1618 The Golden Number.
Goldennumber.net, 20 May 2014. Web. 28
Feb. 2015.